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The British Horological Institute has archived and edited the following from e-mails sent to the Clock/Clockers mailing lists on the Internet. The information here does not necessarily indicate a method approved by the BHI, we are only publishing this digest so that others can decide for themselves whether the methods listed below will suit them.
From: Alan Heugh, George Painter, Jim Sturm
Removing scratches from glass can be a long and tedious job. Here are some suggested techniques.
Method 1
On an individual craftsman's level, polishing glass isn't quick or easy. I have a small diamond lapidary set-up and I've repolished a few thick Hamilton crystals. It took hours.
You have to grind the whole surface down to the bottom of the deepest scratch and then do the same process with each successively finer grit of diamond compound. Generally it's simpler to slightly dome the surface like a shallow cabochon, but if authenticity is important for the value of the watch you should keep a flat crystal flat - which is much harder, requiring a hard lap; it's like cutting one large facet. I doubt if a fancier lapidary machine would help much. On a positive note, I didn't have to remove the crystal from it's case bezel, although This took lots of patient care not to mar the metal.
If the crystal needs replacement it's easier to cut a new crystal from ordinary triple thick window glass - score with a new glass cutter using ice and heat to encourage the crack, and finish grinding/polishing on a lathe for perfection, or by eye with care.
A related thought... I recently read good advise for keeping grit out of machines while grinding - cover the bed and wherever necessary with aluminium foil, conforming it to the machine, and spray it with oil to catch and hold the particles. This works great! If something goes wrong and it gets caught in the machine it just tears, whereas a rag will grab flap and tangle, and possibly include parts of you in the event.
Method 2
A "NEW" item listed called "Watch Crystal Scratch Repair Kit for Plastic and Glass Crystals." The kit is $25. Refills of various items are also available. One person has tried the kit with little success. This is what he said: "I've use that same kit purchased from Cas-Ker and was very disappointed. The sanding discs wore through on the first attempt to polish and left the surface wavy. At $5.00 a throw I'm not inclined to get replacements. The plastic polishing compound seems to work but I get better results from a buffer charged with a crystal polishing compound. I haven't yet use the glass polishing system but fear I will get the same results.
Method 3
Find one of the "eyeglasses in an hour" stores which has some mighty fancy eyeglass grinders busy grinding away, and ask them to polish the crystal
Method 4
You'll need a flat surface on which to put, grit side up, a piece of emery paper of, say, 250 mesh grit. Using a figure-8 motion, grind off the scratches. The crystal will then appear somewhat milky. Carefully clean off any residual grit, set up a 400 mesh paper at a separate location, and polish the milkiness off. There are polishing wheels lubricated with water to do this work, but they cost lots o' money. One undesirable outcome of the hand method will be that the edge of the crystal face will be a bit rounded unless you rig some way to keep the crystal from tipping randomly as you grind and polish. To me, the result is much better than the scratched crystal.
Method 5
Use a compound called cerium oxide which is sold by automotive parts houses for the removal of scratches on windshields. It is used in a buffing process after mixing with water. It does work but requires endless hours of polishing. If the crystal gets too hot in the process it can crack. The chemical is also toxic.